If you use public key crypto in the correct way, then every user has it's own private key and corresponding public key (included in the certificate) and the keys of users are not related. Consequently, compromising the private key of one user does not affect any of the other users. So in the case of compromise of the private key of one user the remaining users are safe.
There are examples where you would run into problems, e.g., if using common modulus for RSA - but if the user's private keys are generated correctly, i.e., independently with independent and good randomness - as it should be done in practice - then there will be no problem. It is, however, known that bad randomness is partially used in practice, e.g., resulting in RSA moduli that share at least a prime factor. You can find more information for example here or another example here.
Clearly, if you use public key crypto in the wrong way and give a private key to several users, then you will have this problem or if you use bad randomness you may also run into these problems. But you should not do that!!